Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces

We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) C-p norm (with p is an element of N boole...

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Detalles Bibliográficos
Autor: Azagra Rueda, Daniel
Tipo de recurso: artículo
Fecha de publicación:1997
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/57010
Acceso en línea:https://hdl.handle.net/20.500.14352/57010
Access Level:acceso abierto
Palabra clave:517.986
Infinite-dimensional Banach space
Unit sphere
Hyperplane
Diffeomorphism
Funciones (Matemáticas)
1202 Análisis y Análisis Funcional
Descripción
Sumario:We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) C-p norm (with p is an element of N boolean OR {infinity}) is C-p diffeomorphic to Y \ {0}.